Coherent-Structure Eigenmodes of the Twisted Bird-Map Ulam Transfer Operator Occupy a Numerical Killing Zone: Two-Axis Calibration Against Ocean and Double-Gyre Controls (Paper 58 in the Non-Holomorphic Fractal Series)

This preprint is part of the Non-Holomorphic Fractal Series (Paper 58). All numerical claims are finite-grid and are derived from seven CSV files stored locally in the author's Linux environment: paper58_killzone_summary.csv, paper58_scan_summary.csv, paper58_doublegyre_precisionscan.csv, paper58_leftgeomscan_doublegyre.csv, paper58_doublegyre_joint_scan.csv, paper58_agulhas_joint_scan.csv, paper58_bird_joint_scan.csv. Every count and threshold in the paper is directly traceable to these files. Researchers who wish to inspect the CSVs are welcome to contact the author. On the finite N × N column-stochastic Ulam transfer matrices derived from the twisted Bird map at ε = 0.70, N = 16384 (WBA and Lorentzian kernels), we apply the two-axis diagnostic protocol of the Non-Holomorphic Fractal Series: precision collapse (δ_j > |λ_j|, equivalently κ_j · ε_mach > |λ_j|) and observable disintegration (σ_j = k90(v_j)/k90(w_j) ≥ 100). We find that 18 of the 20 scanned tiers (all sub-dominant, j = 2, …, 10 across both kernels) satisfy both criteria simultaneously, placing them in the killing zone. Tier 1 is safe on the precision axis but exhibits σ_1 = 14746, confirming observable disintegration of the left eigenvector. As negative controls we scan the Agulhas drifter-derived Ulam operator (N ∈ {2048, 8192, 18432}, 30 tiers) and a rotating double-gyre Ulam operator (N ∈ {2048, 8192, 18432, 32768}, 40 tiers): both controls return zero tiers in the killing zone on every executed grid. The contrast is structural: the Bird-map killing zone arises from the joint occurrence of extreme non-normality and eigenvector support collapse, neither of which is a universal property of non-symmetric Ulam operators on the executed grids.